Transformations of shapes

Tier: #Higher

🔗What you need to know first
How to

There are four transformations you need to know. Each moves or resizes a shape in a specific way, and each requires a precise description to earn full marks.

Translation — slides a shape without rotating or reflecting it. Describe with a column vector $\binom{x}{y}$ where $x$ is right/left and $y$ is up/down.

Reflection — flips a shape in a mirror line. Describe by stating the equation of the mirror line (e.g. $y = x$, $x = 2$).

Rotation — turns a shape about a fixed point. Describe with: angle, direction (clockwise or anticlockwise), and centre of rotation.

Enlargement — scales a shape from a centre point. Describe with: scale factor and centre of enlargement. A fractional scale factor makes the image smaller; a negative scale factor places the image on the opposite side of the centre.

When asked to describe a transformation, give all required information — a partial description (e.g. "rotation" without angle or centre) scores zero.

Common error: giving two transformations when a single one is asked for — one transformation only.

Questions to practise
📝Past paper questions
💬What the examiners say
  • "It was apparent that some students had used tracing paper when answering this question and this was generally a successful strategy for determining the centre of rotation."
⬆️How you can quickly improve
  • For a rotation, always state all three elements: angle, direction (clockwise or anticlockwise), and the centre point as coordinates.
  • Check whether the question says 'a single transformation' — if it does, find the one transformation that achieves the result directly, not a sequence of steps.
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